1

Theoretical Investigation of Air Breakdown Direct 1

Current Triboelectric Nanogenerator 2

Sixing Xu1,2, Hengyu Guo2,3, Steven L. Zhang2, Long Jin2, Wenbo Ding4, Xiaohong 3

Wang1 & Zhong Lin Wang2,3 4

1Department of Microelectronics and Nanoelectronics, Tsinghua University, Beijing 100084, China.2School of 5

Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245, USA. 3Beijing 6

Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 100083, China. 4Tsinghua-7

Berkeley Shenzhen Institute, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 8

518055, China. Correspondence and requests for materials should be addressed to X. W. (email: wxh-9

ime@tsinghua.edu.cn) or to Z.L.W. (email: zhong.wang@mse.gatech.edu) 10

11

12

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

2

Abstract 1

Triboelectric nanogenerator (TENG), which harvests ubiquitous ambient mechanical 2

energy, is a promising power source for the distributed energy. Recently reported new 3

generation direct current TENG (DC-TENG) based on the air breakdown effect has 4

exhibited unique advantages over conventional modes of TENG devices, such as free-5

of-rectification and intrinsic switching behavior. However, owing to different working 6

mechanisms and output characteristics, the existing theory and power management 7

strategies are not suitable for in-depth understanding and further advancement of air 8

breakdown DC-TENG. Herein, a theoretical study and experimental verification that 9

systematically investigate the physics, output characteristics and the power 10

management strategy of air breakdown DC-TENG is presented. A general simulation 11

model is then proposed and verified through a statistical analysis method. Contrary to 12

previous understanding of highly conductive breakdown pathway, a huge resistance is 13

observed and causes inevitable energy loss, which is regarded to be caused by corona 14

discharge. Finally, device optimization and power management strategies are discussed, 15

and a fundamental guidance is given for rational design of air breakdown DC-TENG. 16

17

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

3

Triboelectric nanogenerator (TENG), as a mechanical energy harvester, has been 1

proven to be a promising power alternative for distributed energy due to the features of 2

high power, environmentally friendly and easy-scalable1-9. Over the past few years, 3

TENG devices has been quickly developed and widely applied in numerous 4

applications, including energy harvesting, high-voltage power source, active sensing, 5

human machine interface and etc10-16. Accompanied with the development of TENG, 6

the physical mechanism, simulation model and power management strategy have also 7

been proposed and verified by researchers17-27. These theories serve as effective 8

guidelines and have boosted the advancement of the field. However, it is found that the 9

power efficiency of current TENG devices has hit the wall due to two practical 10

problems: firstly, current TENG devices are easily associated with uncontrolled 11

electrostatic breakdown due to their ultrahigh voltage, so that the generated charge 12

cannot be held and released at the highest voltage28-31; secondly, the output of these 13

TENG devices are featured by alternating current and high matching impedance, which 14

bring inevitable energy loss during the energy conversion process32, 33. 15

Recently, a new generation of TENG based on contact electrification and air 16

breakdown effect has been developed and show great advantage toward conventional 17

modes of TENG34-37. The breakdown process is “one way”, which causes a direct 18

current output, making the rectification module to be unnecessary. In addition, different 19

from previous four modes of TENG, the charges of the air breakdown direct current 20

TENG (DC-TENG) are released with the breakdown potential during the discharge so 21

that energy efficiency can be naturally higher than those being released instantaneously. 22

Some experimental pioneering works have shown the outstanding performances of air 23

breakdown DC-TENG34-36. However, the systematic operation mechanism and 24

optimization path have not been investigated yet, which ascribed to the different physics 25

effects and unfeasibility of conventional theories for the air breakdown DC-TENG. 26

Herein, through both simulation and experiment verification, we report a 27

theoretical research and simulation model for the air breakdown DC-TENG. To 28

overcome the randomness of the breakdown peaks, an automatic statistical analysis and 29

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

4

fitting method is proposed and serve as an effective tool in investigating the theory of 1

the air breakdown DC-TENG. Based on the proposed method, an equivalent circuit of 2

air breakdown DC-TENG is derived, containing a current source, an inner capacitor, a 3

diode, a voltage-controlled gate. Moreover, different from the conventional cognition, 4

which believes that breakdown path should be highly conductive, a large resistance is 5

observed in this circuit model, which causes inevitable energy loss and a slow discharge 6

process. Based on the theoretical model, the power management strategy for such 7

circuit model is investigated, suggesting a potential of up to 100% of power efficiency. 8

Finally, the key challenge and future optimization direction are discussed. 9

10

Recently, several different air breakdown DC-TENG structures have been reported and 11

they are both caused by contact electrification and air discharge effect, which is the 12

basic difference with conventional TENG devices34-37. Similar to the unified simulation 13

model of conventional TENGs38, which greatly facilitate its optimization, a unified 14

model of air breakdown DC-TENG is also need to be developed for the further 15

advancement, standardization and industrialization. One of the most exemplary air 16

breakdown DC-TENG structure36, as illustrated in Figure 1a, is utilized to investigate 17

the theory of air breakdown DC-TENG. When the bottom electrode slides on the 18

dielectric layer, opposite triboelectric charges will be generated due to the contact 19

electrification and then the generated negative charge on the dielectric would induce 20

positive charges on the sharp top electrode7, 8. According to Gauss theorem, the electric 21

field strength near the top electrode can easily exceed the limit of air breakdown, 22

causing ionization of air molecules. Detached electrons will be accelerated by the 23

electric filed and collides with more air molecules. As studied in breakdown theory39, 24

three stages can be roughly divided with the increasing of accumulated charges, as 25

shown in Fig. 1b: 1) turn-off state: the electric field strength is too small for ionization 26

and little current can be transmitted by the near-insulated air; 2) corona discharge state: 27

the electric field strength can ionize air molecule but not enough for breakdown. In this 28

stage, the ionization and recombination rates are competing and reach a balance at a 29

certain distance from the top electrode. From the circuit aspect, a continuous current 30

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

5

will be provided with the movement of the slides, and the current-voltage can be 1

approximated as Townsend relation: 2

3 𝐼 = 𝐴𝑈(𝑈 − 𝑈𝐶) (1) 4

5

where 𝐴 is a structure and environment related constant, 𝑈 is the voltage between 6

top and bottom electrodes and 𝑈𝐶 is the critical voltage for corona discharge; 3) 7

breakdown state: the electric field strength is strong enough to cause an electron 8

avalanche and a conductive pathway between top electrode and dielectric layer will be 9

established. 10

According to above analysis, a simulation circuit model, as shown in Fig. 1c, was 11

proposed. Firstly, a current source and an inner capacitor are proposed to demonstrate 12

the effect of sliding triboelectrification, while a diode is added to describe the ‘one-way’ 13

characteristic of discharge process. Afterward, a voltage-controlled resistor is proposed, 14

representing the variable path resistance during different states. When little charge is 15

accumulated on the top electrode, which is denoted as period one (P1), the gas between 16

top electrode and tribo-layer is unionized, making it behave similar to an insulator, 17

making the resistance extremely large. While the voltage exceeds the ionization critical 18

voltage40, denoted as period two (P2), corona current appears and greatly decreases the 19

resistance39. Furtherly, in the period three (P3), the voltage between top electrode and 20

bottom electrode exceeds the breakdown limitation and the resistance sharply decreases 21

to near zero, representing the short-circuit of the breakdown path. The states of the 22

switching system with controlling voltage can be expressed by Eqs. (2). 23

24

States = { 𝑃1: 𝑅 → ∞; 𝑆𝑤𝑖𝑡𝑐ℎ = 𝑜𝑓𝑓 ( 𝑈 < 𝑈𝐶)𝑃2: 𝑅 = 𝐴𝑈−𝑈𝐶 ; 𝑆𝑤𝑖𝑡𝑐ℎ = 𝑜𝑓𝑓 (𝑈𝐶 < 𝑈 < 𝑈𝐵𝑟𝑒𝑎𝑘) 𝑃3: 𝑅 → 0; 𝑆𝑤𝑖𝑡𝑐ℎ = 𝑜𝑛 (𝑈 > 𝑈𝐵𝑟𝑒𝑎𝑘) (2) 25

26

where 𝑈𝐵𝑟𝑒𝑎𝑘 is the critical electron avalanche voltage which can be predicted by 27

Paschen’s Law. It should be mentioned that, different from previous thoughts which 28

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

6

simply believe the discharge should only be caused by breakdown, we insist that a 1

corona discharge process is inevitable. This corona discharge is significant to current 2

air breakdown DC-TENG, because the released charge in this process is comparable to 3

the triboelectric charge. 4

5

6

7

Figure 1. The operation mechanism and simulation model of air breakdown DC-8

TENG. (a) The concept illustration of basic air breakdown DC-TENG device and 9

operation mechanism. (b) The discharge process with three stages. (c) The simulation 10

circuit model of the air breakdown DC-TENG. 11

12

13

For the investigation of a circuit black box with multiple parameters, testing the output 14

under given inputs and loads and then do the fitting, is the most effective and reliable 15

method. A typical short-circuit current output of the air breakdown DC-TENG is shown 16

in Fig. 2a (see Method for device fabrication and testing). It can be observed that the 17

discharge peaks do not have a fixed magnitude and time interval, but randomly 18

distributed around the mean value, which is resulted from the randomness of the 19

collision of ions. Therefore, it is not rigorous to verify the simulation model through 20

single discharge process, instead statistic method with sufficient data should be used to 21

get convincing results. The detailed structure of the peak is demonstrated in Fig. 2(b) 22

(c). As each discharge peak is caused by capacitive charge/discharge process, the 23

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

7

current/voltage should obey the form of negative exponential, as listed in Eqs. (3), and 1

the half-life period should be written as Eqs. (4). 2

3 𝑉 = 𝑉0𝑒− 𝑡𝑅𝐶 = 𝑉0𝑒− 𝑡(𝑅𝑇𝐸+𝑅𝐸𝑋)𝐶𝑇𝐸 (3) 4

5 𝑇ℎ𝑎𝑙𝑓 = ln(2) 𝐶𝑇𝐸𝑅𝑇𝐸 + ln(2) 𝐶𝑇𝐸𝑅𝐸𝑋 (4) 6

7

where 𝑉0 is the initial voltage, 𝑅𝑇𝐸 and 𝐶𝑇𝐸 are the intrinsic resistance and 8

capacitance, 𝑅𝐸𝑋 is the external load resistance and 𝑇ℎ𝑎𝑙𝑓 is the half-life period. An 9

automatic program for peak acquisition and analysis was developed, of which the 10

algorithm is shown in Supplementary Scheme 1 (code is available in Supplementary 11

Code 1). Specifically, each peak can be detected automatically by comparing the data 12

point with data before and after, with a minimum peak width and height thresholds. 13

After that, the half-life period is obtained by traverse all data points and select the 14

closest one. As the time constants of a capacitive charge/discharge circuit is 15

proportional to the resistance, a systematic test was done to investigate different 16

external resistance and its relationship with the peak’s half-life periods. The current 17

output with load resistances of 100M Ω and 10G Ω are shown in Fig. 2(d)(e), with the 18

detailed peak shapes insets. It is clear that the half-life periods obviously increase with 19

the increase of external resistance. Interestingly, with the external resistance of 10G Ω, 20

the current did not drop to zero for each peak due to a slow discharge process, but it 21

contributes a stable base current, which can be a solution for stable DC output33. The 22

analysis of the time constants with the three representative external resistances (short-23

circuit, 100M Ω and 10G Ω) is shown in Fig. 2f, showing the mean time constants of 24

2.3 ms, 4.5 ms and 134.8 ms, respectively. In addition, the standard deviations of those 25

time constants are only 0.36 ms, 0.71 ms and 14.7 ms, demonstrating the high reliability 26

and repeatability of the calculated time constants. 27

The fitting of the time constants with different external resistances is shown in Fig. 28

2g. As expected, the fitting curve demonstrates a correlation coefficient as high as 0.997, 29

which strongly validates the capacitive discharge hypothesis. Accordingly, the intrinsic 30

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

8

capacitance and resistance are calculated to be 21.812 pF and 157.75 MΩ, respectively. 1

The magnitude of capacitance is in accordance to the expectation; however, the 2

resistance is much larger than it should be for a breakdown conductive path, which 3

generally below 10 Ω for the millimeter-level distance. It is reasonable to believe that 4

the corona discharge plays an important role during the discharge process. The 5

transferred charge with operation periods is shown in Fig. 2h, in which the charge 6

transferred in operation cycles is kept almost constant, indicating the high stability with 7

sufficient amount of random discharge peaks. Moreover, with the increase of the move 8

speed, i.e. increase of the operation frequency, the transferred charge decreases, which 9

should be ascribed to the time interval is too short for the release of the charge. 10

11

12

13

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

9

1

Figure 2. The outputs analysis of air breakdown DC-TENG. (a) Short-circuit 2

current output of air breakdown DC-TENG. (b)(c) Detailed curve shape of the 3

discharge peak, with (c) the half-life period detecting and fitting method. (d) The 4

current output with load resistance of 100M Ω. (e) The current output with load 5

resistance of 10G Ω. (f) The mean value and standard deviation of half-life periods with 6

load resistances of 0 Ω(purple), 100M Ω(red) and 10G Ω(blue). (g) The fitting of half-7

life periods with different external resistances. (h) The transferred charges with 8

different slider moving speed (moving distance is fixed by 6 cm). All the tests in (a)-(g) 9

are carried out with period of 60s. 10

11

12

Switch-mode power techniques are the most widely used DC-DC conversion methods 13

in power management circuits and have also been successfully applied to boost the 14

performance of TENG devices41,42. However, introducing an external electronic switch 15

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

10

for TENG is difficult due to the limitation of the threshold voltage and channel 1

capacitance of electronic switches. Also, mechanical switch generally exhibits long 2

response time, causing non-ideal discharge during the switching process. Another issue 3

is that it is difficult to detect whether the voltage output is at the peak through electronic 4

switch, which is the key for the power management strategy. Therefore, the air 5

breakdown DC-TENG with naturally switching feature is promising to reduce the 6

complexity of power management circuit and perform high power efficiency. 7

Nevertheless, due to the intrinsic resistance brought by the discharge process, current 8

air breakdown DC-TENG devices do not show the potential benefit. The power output 9

with various load resistances is shown in Fig. 3a, indicating a matching impedance 10

around 2G Ω, which should be much lower for an ideal switching system. In addition, 11

the simulation of the power output for each discharge process with the parameters listed 12

in Supplementary Table. 1 and time interval of 0/10/20/50 ms is shown. The experiment 13

results are well fitted with the circuit simulation with 20 ms intervals between each 14

discharge process, which strongly proves the simulation model again. 15

Even though considerable resistance exists in current air breakdown DC-TENG, 16

there is still a significant advantage for power management. The basic idea of utilizing 17

the switching feature of the air breakdown DC-TENG for power management is 18

illustrated in Fig. 3b. When the peak discharge occurred, the switch is turned on and the 19

charge accumulated flows through the external inductor Lex to the load. In this case the 20

device output is prevented from increasing immediately to its peak value as the inductor 21

stores energy taken from the increasing output. Meanwhile, charge on Cex builds up 22

gradually during the ‘on’ period. As the accumulated charge been released, the switch 23

is turned off. In this stage, the energy stored in the magnetic field around Lex and in the 24

electric field around Cex are released back to the load. In such, the original pulse output 25

with high voltage can be turned to stable output with applicable voltage level. The 26

efficiency of the proposed power management circuit can be calculated based on the 27

state Eqs. (5): 28

29

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

11

𝑄𝑇𝐸𝐶𝑇𝐸 + 𝑅𝑇𝐸 𝑑𝑄𝑇𝐸𝑑𝑡 + 𝐿 𝑑2𝑄𝑇𝐸𝑑𝑡2 = 𝑉0 (5) 1

2

where 𝑄𝑇𝐸 is the charge for each release process, 𝑅𝑇𝐸 and 𝐶𝑇𝐸 are the intrinsic 3

resistance and capacitance, 𝐿 is the external inductor and 𝑉0 is the stable voltage of 4

the external capacitor. The energy transferred to the load and the power efficiency can 5

be calculated (see detail in Supplementary Note 1). The power efficiency is defined as: 6 η = 𝐸𝑇𝐸−𝐸𝑅−𝐸𝑐𝐸𝑇𝐸 (6) 7

where 𝐸𝑇𝐸 is the system energy capacitive energy before discharge, 𝐸𝑐 is the system 8

capacitive energy remained after discharge, and 𝐸𝑅 is the energy wasted on the inner 9

resistor. Fig. 3c plots the power efficiency versus the quality factor 4𝐿/𝑅2𝐶. It can be 10

observed that the efficiency is negatively related with the intrinsic resistance, yet 11

positively related to the external inductance. With the increase of the quality factor, the 12

power efficiency will gradually increase to about 40% with 4𝐿/𝑅2𝐶 = 10, and nearly 13

100% when 4𝐿/𝑅2𝐶 >1000. The effectiveness of such power management strategy is 14

furtherly verified through circuit simulation (Supplementary Fig. S2). 15

16

17

Figure 3. The power output and management strategy for air breakdown DC-18

TENG. (a) The power out with different external resistances and simulations with 19

different time interval between peaks. (b) The proposed circuit scheme for the power 20

management. (c) The theoretical power efficiency of the power management circuit and 21

circuit simulation result. 22

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

12

1

2

From the above analysis, it is clear to see the resistance caused by corona discharge 3

is the main obstacle for achieving high power efficiency in real applications. Therefore, 4

the main effort should been put into reducing the charge been released through corona 5

discharge, i.e. make the breakdown process been the dominant discharge route. 6

Moreover, the impact of device structure to the simulation model is also investigated 7

through controlled experiments, as shown in Supplementary discussion. In such, 8

several potential strategies can be carried out in the future device development: 1) 9

increase the charge accumulation rate so that the corona discharge process can be 10

shorter. To this end, methods like increasing the surface charge density and mechanical 11

operation speed can be effective; 2) decrease the breakdown avalanche critical voltage. 12

Similarly, this method can also reduce the corona discharge loss. Therefore, adjusting 13

device structure and atmosphere to approach the lowest point according to the 14

Paschen’s Law can be the answer; 3) skip the corona discharge process. The most 15

efficient strategy is to accumulate the charge without discharge, until it meets the 16

requirement of breakdown. 17

In conclusion, we have systematically investigated the operation mechanism of air 18

breakdown DC-TENG and especially pointed out the inevitability of the corona 19

discharge process and related resistance in simulation model. Based on sufficient 20

amount of half-periods time with various external resistances, the capacitive discharge 21

model has been well fitted with a correlation efficient of 0.997, strongly proved the 22

hypothesis of discharge model. Based on the simulation model, the potential power 23

management strategies for air breakdown DC-TENG are discussed, showing that in 24

spite of the intrinsic resistance, high power efficiency could also be obtained with 25

external inductor. At last, we point out the key for future optimization of air breakdown 26

DC-TENG is to reduce the corona discharge and improve the breakdown, so that the 27

power efficiency can be greatly boosted. We believe that after the establishment of the 28

theoretical model, the air breakdown DC-TENG will be greatly boosted and exhibits its 29

huge potential in power sources, active sensing and all related fields. 30

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

13

Supplementary material: 1

See the supplementary material for the signal analysis algorithm, device fabrication, output 2

measurement, the impact of device structure and the theoretical calculation of power efficiency. 3

4

This work was supported by the National Natural Science Foundation of China (Grant No. 5

61834003, 61531166006), the 973 Program of China (Grant No. 2015CB352106) and the 6

Hightower Chair foundation. S. X. thanks China Scholarship Council for supplying oversea 7

scholarship (201806210286). 8

9

Data availability: 10

The data that support the plots within this paper and other finding of this study are available 11

from the corresponding authors upon reasonable request. 12

13

References: 14

1. F.-R. Fan, Z.-Q. Tian and Z. L. Wang, Nano energy, 2012, 1, 328-334. 15

2. H. Guo, M.-H. Yeh, Y. Zi, Z. Wen, J. Chen, G. Liu, C. Hu and Z. L. Wang, ACS nano, 2017, 11, 4475-16

4482. 17

3. Z. L. Wang, J. Chen and L. Lin, Energy Environmental Science, 2015, 8, 2250-2282. 18

4. Z. L. Wang, ACS nano, 2013, 7, 9533-9557. 19

5. Z. L. Wang, Materials Today, 2017, 20, 74-82. 20

6. Z. L. Wang, Nano Energy, 2018, 54, 477-483. 21

7. Z. L. Wang, Nano Energy, 2020, 68, 104272. 22

8. C. Xu, Y. Zi, A. C. Wang, H. Zou, Y. Dai, X. He, P. Wang, Y. C. Wang, P. Feng and D. Li, Advanced 23

Materials, 2018, 30, 1706790. 24

9. Z. L. Wang, Nano Energy, 2019, 58, 669-672. 25

10. J. Wang, S. Li, F. Yi, Y. Zi, J. Lin, X. Wang, Y. Xu and Z. L. Wang, Nature communications, 2016, 7, 26

1-8. 27

11. W. Ding, J. Zhou, J. Cheng, Z. Wang, H. Guo, C. Wu, S. Xu, Z. Wu, X. Xie and Z. L. Wang, Advanced 28

Energy Materials, 2019, 9, 1901320. 29

12. G. Liu, H. Guo, S. Xu, C. Hu and Z. L. Wang, Advanced Energy Materials, 2019, 9, 1900801. 30

13. L. Jin, B. Zhang, L. Zhang and W. Yang, Nano Energy, 2019, 104086. 31

14. N. Arora, S. L. Zhang, F. Shahmiri, D. Osorio, Y.-C. Wang, M. Gupta, Z. Wang, T. Starner, Z. L. Wang 32

and G. D. Abowd, Proceedings of the ACM on Interactive, Mobile, Wearable, 2018, 2, 1-28. 33

15. M. Xu, P. Wang, Y. C. Wang, S. L. Zhang, A. C. Wang, C. Zhang, Z. Wang, X. Pan and Z. L. Wang, 34

Advanced Energy Materials, 2018, 8, 1702432. 35

16. S. L. Zhang, M. Xu, C. Zhang, Y.-C. Wang, H. Zou, X. He, Z. Wang and Z. L. Wang, Nano Energy, 36

2018, 48, 421-429. 37

17. S. Niu, Y. Liu, X. Chen, S. Wang, Y. S. Zhou, L. Lin, Y. Xie and Z. L. Wang, Nano Energy, 2015, 12, 38

760-774. 39

18. S. Niu, Y. Liu, S. Wang, L. Lin, Y. S. Zhou, Y. Hu and Z. L. Wang, Advanced materials, 2013, 25, 40

6184-6193. 41

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

14

19. S. Niu, Y. Liu, S. Wang, L. Lin, Y. S. Zhou, Y. Hu and Z. L. Wang, Advanced Functional Materials, 1

2014, 24, 3332-3340. 2

20. S. Niu, S. Wang, L. Lin, Y. Liu, Y. S. Zhou, Y. Hu and Z. L. Wang, Energy Environmental Science, 3

2013, 6, 3576-3583. 4

21. S. Niu and Z. L. Wang, Nano Energy, 2015, 14, 161-192. 5

22. Y. Zi, S. Niu, J. Wang, Z. Wen, W. Tang and Z. L. Wang, Nature communications, 2015, 6, 1-8. 6

23. Y. Zi, J. Wang, S. Wang, S. Li, Z. Wen, H. Guo and Z. L. Wang, Nature communications, 2016, 7, 1-7

8. 8

24. S. Wang, L. Lin, Y. Xie, Q. Jing, S. Niu and Z. L. Wang, Nano letters, 2013, 13, 2226-2233. 9

25. W. Liu, Z. Wang, G. Wang, G. Liu, J. Chen, X. Pu, Y. Xi, X. Wang, H. Guo and C. Hu, Nature 10

communications, 2019, 10, 1-9. 11

26. J. Peng, S. D. Kang and G. J. Snyder, Science advances, 2017, 3, eaap8576. 12

27. A. Ghaffarinejad, J. Y. Hasani, R. Hinchet, Y. Lu, H. Zhang, A. Karami, D. Galayko, S.-W. Kim and 13

P. Basset, Nano Energy, 2018, 51, 173-184. 14

28. J. Fu, X. Xia, G. Xu, X. Li and Y. Zi, ACS nano, 2019, 13, 13257-13263. 15

29. X. Xia, J. Fu and Y. Zi, Nature communications, 2019, 10, 1-9. 16

30. J. Wang, C. Wu, Y. Dai, Z. Zhao, A. Wang, T. Zhang and Z. L. Wang, Nature communications, 2017, 17

8, 1-8. 18

31. Y. Zi, C. Wu, W. Ding and Z. L. Wang, Advanced Functional Materials, 2017, 27, 1700049. 19

32. S. Xu, L. Zhang, W. Ding, H. Guo, X. Wang and Z. L. Wang, Nano Energy, 2019, 66, 104165. 20

33. C. Chen, L. Chen, Z. Wu, H. Guo, W. Yu, Z. Du and Z. L. Wang, Materials Today, 2020, 32, 84-93. 21

34. G. Cheng, H. Zheng, F. Yang, L. Zhao, M. Zheng, J. Yang, H. Qin, Z. Du and Z. L. Wang, Nano 22

Energy, 2018, 44, 208-216. 23

35. J. Luo, L. Xu, W. Tang, T. Jiang, F. R. Fan, Y. Pang, L. Chen, Y. Zhang and Z. L. Wang, Advanced 24

Energy Materials, 2018, 8, 1800889. 25

36. D. Liu, X. Yin, H. Guo, L. Zhou, X. Li, C. Zhang, J. Wang and Z. L. Wang, Science advances, 2019, 26

5, eaav6437. 27

37. Y. Yang, H. Zhang and Z. L. Wang, Advanced Functional Materials, 2014, 24, 3745-3750. 28

38. S. Niu, Y. S. Zhou, S. Wang, Y. Liu, L. Lin, Y. Bando and Z. L. Wang, Nano Energy, 2014, 8, 150-29

156. 30

39. Y. Raizer, Spark discharge, Routledge, 2017. 31

40. A. S. Gibson, J. A. Riousset and V. P. J. N. E. R. P. S. A. R. J. Pasko, 2009, 7, 1-17. 32

41. S. Xu, W. Ding, H. Guo, X. Wang and Z. L. Wang, Advanced Energy Materials, 2019, 9, 1900772. 33

42. S. Xu, W. Liu, B. Hu and X. Wang, Nano Energy, 2019, 58, 803-810. 34

35

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539

Thi

s is

the

auth

or’s

pee

r re

view

ed, a

ccep

ted

man

uscr

ipt.

How

ever

, the

onl

ine

vers

ion

of r

ecor

d w

ill b

e di

ffere

nt fr

om th

is v

ersi

on o

nce

it ha

s be

en c

opye

dite

d an

d ty

pese

t.

PL

EA

SE

CIT

E T

HIS

AR

TIC

LE

AS

DO

I: 1

0.1

063/5

.0011539